Optical Isomerism in [Cr(en)3]Cl3

Introduction:
Optical isomerism is a form of stereoisomerism that arises due to the presence of chiral centers in a molecule. Chiral centers are carbon atoms that are bonded to four different groups. Optical isomers, also known as enantiomers, are non-superimposable mirror images of each other. They exhibit different optical activities and have the ability to rotate the plane of polarized light in opposite directions.

[Cr(en)3]Cl3:
[Cr(en)3]Cl3 is a coordination compound that consists of a central chromium atom (Cr) surrounded by three ethylenediamine ligands (en) and three chloride ions (Cl). The ethylenediamine ligand is a bidentate ligand, meaning it can bind to the central metal atom through two lone pairs of electrons.

Chirality in [Cr(en)3]Cl3:
In [Cr(en)3]Cl3, the chromium atom is octahedrally coordinated by the three ethylenediamine ligands and three chloride ions. Each ethylenediamine ligand is attached to the central chromium atom through two nitrogen atoms.

Chiral Centers:
Within each ethylenediamine ligand, there are two nitrogen atoms bonded to different groups: one nitrogen atom is bonded to two hydrogen atoms, while the other nitrogen atom is bonded to a carbon atom and a hydrogen atom. As a result, each ethylenediamine ligand has two chiral centers.

Formation of Optical Isomers:
Since [Cr(en)3]Cl3 consists of three ethylenediamine ligands, each with two chiral centers, the total number of possible optical isomers can be calculated using the formula 2^n, where n is the number of chiral centers.

In this case, there are 6 chiral centers (2 chiral centers per ethylenediamine ligand x 3 ethylenediamine ligands), resulting in 2^6 = 64 possible stereoisomers.

Optical Activity:
Each of these 64 stereoisomers exists as a pair of enantiomers, which are non-superimposable mirror images of each other. Enantiomers exhibit different optical activities, meaning they rotate the plane of polarized light in opposite directions. One enantiomer will rotate the plane of polarized light clockwise (dextrorotatory or +), while the other enantiomer will rotate it counterclockwise (levorotatory or -).

Conclusion:
In summary, [Cr(en)3]Cl3 exhibits optical isomerism due to the presence of six chiral centers within the three ethylenediamine ligands. The compound can exist as a total of 64 stereoisomers, each consisting of a pair of enantiomers with different optical activities. Optical isomerism in [Cr(en)3]Cl3 is an important aspect to consider when studying its chemical and biological properties.

En is bidented ligand thus it has d and l form